I get my FC3 via two methods. The first is buying and breaking down bridesmaid sandals in Ul'dah specifically because they also return spruce lumber. The return rate on FC3s is about 20% from my experience.

The second method is crafting butt loads of spicy tomato relish, which does stack, and trade them in for artisans spectacles from Talan in Mor Dhona and then desynth them. The ingredients for the relish are easily obtained with just one nabbed via unspoiled node. However Dzamael tomato's are also usually dirt cheap on MB being a common return from BTN retainer ventures. The drawback is the return rate on FC3s is much lower on these than the Mastercraft Demimaterias. However just toss those up on the MB and buy the FC3s at a mitigated loss, or perhaps even a profit depending on prices on your server.

I advise against purchasing artisan tools to desynth because they are unique, forcing you to trade with Talan for each attempt. If you've ever done this, you know how quickly it becomes tedious.

One more option: buy and desynth wall lanterns from housing districts. These don't return FC3s, but they do return FC2s, cobalt ingots, and frosted glass lenses. Sell those and buy up the FC3s.

You'll obviously be forced to desynth if there is a low supply of FC3 on your server.